Consider first a bipartite quantum state \(\rho ^{AB}\)  of dimension \(d_{A}\times d_{B}\)  acting on a Hilbert space \(H_{A}\otimes H_{B}\) , and let \(K_{A}=K_{A}\otimes _{B}\)  be a local observable on a single part \(A\) . The dynamics of the density matrix \(\rho ^{AB}\)  is governed by the local phase shift transformation \(e^{-i\theta K_{A}}\) , i.e., \(\rho _{\theta }^{AB}=e^{-i\theta K_{A}}\rho ^{AB}e^{i\theta K_{A}}\) . Quantum Fisher information via local measurements and via local observables, \({\cal F}\left(\rho ^{AB},K_{A} \right)\) , is called local quantum Fisher information on the sub-system \(A\) . When \({\cal F}\left(\rho ^{AB},K_{A} \right)=0\) , then no information can be obtained by measurement because no change in the evolution will be observed. Building on this, the local quantum Fisher information captures the amount of quantum correlations that exist in a given quantum state and allows to quantify the non-classical correlations in terms of quantum Fisher information [1]}. It is defined as the minimum quantum Fisher information over all local observables with respect to the subsystem \(A\)  and given by
\({\cal Q}_{F}\left(\rho ^{AB}\right)=\min _{K_{A}}{\cal F}\left(\rho ^{AB},K_{A}\right).\) 
